Descriptor Covariance and Correlation Hierarchy in Moiré Exciton Photoluminescence

Abstract

We develop a minimal theory for the spatial organization of photoluminescence spectra in moiré transition-metal dichalcogenide heterobilayers. Motivated by hyperspectral mapping of MoSe$_2$/WSe$_2$, which reveals micron-scale correlations among nine peak-decomposition-free spectral descriptors, we propose a descriptor-based disorder-filter picture in which different descriptors probe different components of a multi-scale disorder landscape, producing a hierarchy of spatial correlation lengths. The central result is the correlation hierarchy $ξ(E_{\rm cent}) \ge ξ(E_{\rm dom})$, derived from the decomposition of the dominant-peak energy into a smooth background contribution and a short-range trap-switching fluctuation term. The same framework explains the principal inter-descriptor Spearman correlations, including the near-perfect anti-correlation $ρ_{\rm S}(ΔE_{\rm cd}, R_{\rm HL}) \approx -0.978$ as a robust spectral-shape relation for spectra with a dominant unimodal envelope. The framework provides a peak-decomposition-free route to infer effective disorder parameters from hyperspectral data through the descriptor covariance structure, without microscopic line assignment.